1. Field of the Invention
The present invention relates to programming of quantum computing algorithms, and use of quantum computing algorithms in connection with control systems based on quantum soft computing.
2. Descriiption of the Related Art
The interplay between mathematics and physics has always been beneficial to both fields of endeavor. The calculus was developed by Newton and Leibniz in order to understand and describe dynamical law of motion of material bodies. In general, geometry and physics have had a long and successful symbiotic relationship: classical mechanics and Newton""s gravity are based on Euclidean geometry, whereas in Einstein""s theory of general relativity the basis is provided by non-Euclidean, Riemannian geometry (an important insight taken from mathematics into physics). Although this link between physics and geometry is still extremely strong, one of the most striking connections today is between information theory and quantum physics. There appears to be a trend to make mathematics more xe2x80x9cphysical.xe2x80x9d
Computation, based on the laws of classical physics, leads to completely different constraints on information processing than computation based on quantum mechanics (as first realized by Feymann and Deutsch). Computation seems to be the only commodity ever to become exponentially better (e.g., faster) as it gets cheaper. In the past few decades, information handling capacity has grown at a rate ten million times faster than that of the human nervous systems during the four billion years since life began on Earth. Yet the theory and technology of computing has rested for more than 50 years on the Turing-machine model of computation, which leads to many intractable or undecidable problems.
Quantum computers hold promise for solving such intractable problems, but, unfortunately, there currently exist no algorithms for xe2x80x9cprogrammingxe2x80x9d a quantum computer. Calculation in a quantum computer, like calculation in a conventional computer, can be described as a marriage of quantum hardware (the physical embodiment of the computing machine itself, such as quantum gates and the like), and quantum software (the computing algorithm implemented by the hardware to perform the calculation). To date, quantum software algorithms, such as Shor""s algorithm, used to solve problems on a quantum computer have been developed on an ad hoc basis without any real structure or programming methodology.
This situation is somewhat analogous to attempting to design a conventional logic circuit without the use of a Karnough map. A logic designer, given a set of inputs and corresponding desired outputs, could design a complicated logic circuit using NAND gates without the use of a Karnough map. However, the unfortunate designer would be forced to design the logic circuit more or less by intuition, trial, and error. The Karnough map provides a structure and an algorithm for manipulating logical operations (AND, OR, etc.) in a manner that allows a designer to quickly design a logic circuit that will perform a desired logic calculation.
The lack of a programming or design methodology for quantum computers severely limits the usefulness of the quantum computer. Moreover, it limits the usefulness of the quantum principles, such as superposition, entanglement and interference, that give rise to the quantum logic used in quantum computations. These quantum principles suggest, or lend themselves, to problem-solving methods that are not used in conventional computers.
These quantum principles can be used with conventional computers in much the same way that genetic principles of evolution are used in genetic optimizers today. Nature, through the process of evolution, has devised a useful method for optimizing large-scale nonlinear systems. A genetic optimizer running on a computer efficiently solves many previously difficult optimization problems by simulating the process of natural evolution. Nature also uses the principles of quantum mechanics to solve problems, including optimization-type problems, searching-type problems, selection-type problems, etc. through the use of quantum logic. However, the quantum principles, and quantum logic, have not been used with conventional computers because no method existed for programming an algorithm using the quantum logic.
The present invention solves these and other problems by providing a methodology and an algorithm for programming an algorithm to solve a problem using quantum logic. The quantum logic program can be xe2x80x9crunxe2x80x9d on a quantum computer. The algorithm can also be xe2x80x9crunxe2x80x9d on a non-quantum computer by using the non-quantum computer to simulate a quantum computer. This allows the concepts, features, and principles of quantum computing, such as superposition, entanglement, quantum interference, and the like (and the massive parallelism enabled by these principles) to be used to advantage in non-quantum computers without the need to develop quantum computer hardware.
In one embodiment, the quantum programming method is used to with a genetic search algorithm in a control system. A conventional genetic search algorithm searches for an optimal solution in a single space. The quantum search algorithm provides global searching for an optimum solution among many spaces.
In one embodiment, an algorithm design for quantum soft computing is designed by encoding an input function ƒ into a unitary matrix operator UF. The operator UF is embedded into a quantum gate G, where G is a unitary matrix. The gate G is applied to an initial canonical basis vector to produce a basis vector. The basis vector is measured. These steps are repeated several times as necessary to generate a set of measured basis vectors. The measured basis vectors are decoded and translated into an output vector.
In one embodiment, the encoding into UF includes transforming a map table of ƒ into an injective function F, transforming the map table of F into a map table for UF, and transforming the map table for UF into UF.
In one embodiment, the Shannon entropy of the basis vectors is minimized.
In one embodiment, an intelligent control system having a quantum search algorithm to reduce Shannon entropy includes a genetic optimizer to construct local solutions using a fitness function configured to minimize a rate of entropy production of a controlled plant. A quantum search algorithm is used to search the local solutions to find a global solution using a fitness function configured to minimize Shannon entropy.
In one embodiment, global solution includes weights for a fuzzy neural network. In one embodiment, the fuzzy neural network is configured to train a fuzzy controller, and the fuzzy controller provides control weights to a proportional-integral-differential (PID) controller. The PID controller controls a plant.
In one embodiment, a quantum search algorithm is evolved according to a fitness function selected to minimize Shannon entropy.
In one embodiment, quantum search algorithm is evolved by minimizing Heisenberg uncertainty and minimizing Shannon entropy.
In one embodiment, a quantum search evolves by applying an entanglement operator to create a plurality of correlated state vectors from a plurality of input state vectors and applying an interference operator to the correlated state vectors to generate an intelligent state vector, where the intelligent state vector has less classical entropy than the correlated state vectors.
In one embodiment, global optimization to improve a quality of a sub-optimal solution is accomplished by applying a first transformation to an initial state to produce a coherent superposition of basis states. A second transformation is applied to the coherent superposition using a reversible transformation to produce coherent output state. A third transformation is applied to the coherent output states to produce an interference of output states and a global solution is selected from the interference of output states. In one embodiment, the first transformation is a Hadamard rotation. In one embodiment, each of the basis states is represented using qubits. In one embodiment, the second transformation is a solution to Shrodinger""s equation. In one embodiment, the third transformation is a quantum fast Fourier transform. In one embodiment, selecting is made to find a maximum probability. In one embodiment, the superposition of input states includes a collection of local solutions to a global fitness function.